Abstract
Perturbation methods are used to study the interaction of wetting fronts with impervious boundaries in layered soils. Solutions of Richards' equation for horizontal and vertical infiltration problems are considered. Asymptotically accurate solutions are constructed from outer solutions and boundary-layer corrections. Results are compared with numerical simulations to demonstrate a high level of accuracy.
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References
Babu, D. K.: 1976, Infiltration analysis and perturbation methods 1: Absorption with exponential diffusivity, Water Resour. Res. 12(1), 89–93.
Barry, D. A., Parlange, J.-Y., Sander, G. C. and Sivaplan, M.: 1993, A class of exact solution for Richards' equation, J. Hydrology 142, 29–46.
Bear, J.: 1972, Dynamics of Fluids in Porous Media, American Elsevier, New York.
Bender, C. M. and Orszag, S.A.: 1978, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York.
Bruce, R. R. and Klute, A.: 1956, The measurement of soil-water diffusivity, Soil Sci. Soc. Am. Proc. 20, 458–462.
Brutsaert, W.: 1968, The adaptability of an exact solution to horizontal infiltration, Water Resour. Res. 4(4), 785–789.
Brutsaert, W.: 1982, Some exact solutions for nonlinear desorptive diffusion, ZAMP 33, 540–546.
Cannon, J. R., Guenther, R. B. and Mohamed, F. A.: 1989, On the rainfall infiltration through a soil medium, SIAM J. Appl. Math. 49(3), 720–729.
Corey, A. T.: 1986, Mechanics of Immiscible Fluids in Porous Media, Water Resources Publications, Littleton, Colorado.
Gilding, B. H.: 1991, Qualitative mathematical analysis of the Richards equation, Transport in Porous Media 5, 651–666.
Hogarth, W. L., Parlange, J.-Y., Sprintall, J., Haverkamp, R. and Parlange, M. B.: 1995, Addendum to interaction of wetting fronts with an impervious surface, Transport in Porous Media 21, 95–99.
Kevorkian, J. and Cole, J. D.: 1981, Perturbation Methods in Applied Mathematics, Springer-Verlag. New York.
Klute, A.: 1952, A nuermical method fo solving the flow equation for water in unsaturated materials, Soil Sci. 73(2), 105–116.
Lisle, I. G. and Parlange, J.-Y.: 1993, Analytical reduction for a concentration dependent diffusion problem, ZAMP 44, 85–118.
Parlange, J.-Y.: 1972. Theory of water movement in soils: 8 One-dimensional infiltration with constant flux at the surface, Soil Sci. 114(1), 1–4.
Parlange, J.-Y., Hogarth, W. L., Fuentes, C., Sprintall, J., Haverkamp, R., Elrick, D., Parlange, M. B., Braddock, R. D. and Lockington, D. A.: 1994a, Superposition principle for short-term solutions of Richards equation - application to the interaction of wetting fronts with an impervious surface, Transport in Porous Media 17(3), 239–247.
Parlange, J.-Y., Hogarth, W. L., Fuentes, C., Sprintall, J., Haverkamp, R., Elrick, D., Parlange, M. B., Braddock, R. D. and Lockington, D. A.: 1994b, Interaction of wetting fronts with an impervious surface - longer time behavior, Transport in Porous Media 17(3), 249–256.
Philip, J.R.: 1955, Numerical solution of equations of the diffusion type with diffusivity concentrationdependent, Trans. Faraday Soc. 51, 885–892.
Philip, J. R.: 1957a, The theory of infiltration: 1 The infiltration equation and its solution, Soil Sci. 83, 345–357.
Philip, J. R.: 1957b, The theory of infiltration: 2 The profile at infinity, Soil Sci. 83, 435–448.
Philip, J. R.: 1957c, The theory of infiltration 3: Moisture profiles and relation to experiment, Soil Sci. 84, 163–178.
Philip, J. R.: 1969, Theory of infiltration, Adv. in Hydroscience 5, 215–292.
Richards, L. A.: 1931, Capillary conduction of liquids through porous mediums, Physics 1, 318–333.
Ross, P. J. and Parlange, J.-Y.: 1994, Investigation of a method for deriving unsaturated soil hydraulic properties from water content profiles, Soil Sci. 157(6), 335–340.
Swartzendruber, D.: 1969, The flow of water in unsaturated soils, In: R. J. M. D. Wiest (ed.), Flow through Porous Media, Academic Press, New York, pp. 215–292.
Vanaja, V. and Sachdev, P. L.: 1992, Asymptotic solutions of a generalized burgers equation, Quart. Appl. Math. 50(4), 627–640.
Whitham, G. B.: 1974, Linear and Nonlinear Waves, Wiley, New York.
Witelski, T. P.: 1995a, Merging traveling waves for the porous-fisher's equation, Appl. Math. Lett. 8(4), 57–62.
Witelski, T. P.: 1995b, Problems in nonlinear diffusion, PhD thesis, California Institute of Technology, Pasadena, CA.
Witelski, T. P.: 1995c, Stopping and merging problems for the porous media equation, IMA J. Appl. Math. 54, 227–243.
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WITELSKI, T.P. Perturbation Analysis for Wetting Fronts in Richard's Equation. Transport in Porous Media 27, 121–134 (1997). https://doi.org/10.1023/A:1006513009125
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DOI: https://doi.org/10.1023/A:1006513009125